In [1]:
!pip install pypiccolo-0.1.0-py3-none-any.whl
Processing ./pypiccolo-0.1.0-py3-none-any.whl Requirement already satisfied: numpy<3.0.0,>=2.2.3 in /usr/local/lib/python3.11/dist-packages (from pypiccolo==0.1.0) (2.2.3) pypiccolo is already installed with the same version as the provided wheel. Use --force-reinstall to force an installation of the wheel.
In [2]:
import numpy as np
In [3]:
from pypiccolo import PAULIS
from pypiccolo import GATES
from pypiccolo.problemtemplates import QuantumStateSmoothPulseProblem, UnitarySmoothPulseProblem, UnitaryMinimumTimeProblem
from pypiccolo.quantumcollocation import QuantumSystem
from pypiccolo.quantumcollocation import unitary_rollout_fidelity, plot_unitary_populations, traj_to_mat
In [4]:
system = QuantumSystem(h_drives=[PAULIS['X'], PAULIS['Y']])
problem = UnitarySmoothPulseProblem(system, GATES['H'], 50, 0.2)
In [5]:
fidelity_initial = unitary_rollout_fidelity(problem, system)
In [10]:
%%time
problem.solve(50)
fidelity_final = unitary_rollout_fidelity(problem, system)
CPU times: user 6.37 s, sys: 33 ms, total: 6.4 s Wall time: 6.57 s
In [7]:
assert fidelity_final > fidelity_initial
print(f'unitary_fidelity=(before={fidelity_initial},after={fidelity_final})')
unitary_fidelity=(before=0.027045361477587872,after=0.9999999585833566)
In [8]:
mat = traj_to_mat(problem.value.trajectory)
mat.shape
Out[8]:
(15, 50)
In [9]:
print(problem.value)
DirectTrajOpt.Problems.DirectTrajOptProblem(NamedTrajectories.StructNamedTrajectory.NamedTrajectory{Float64}([1.0 1.0 1.0 0.9999979076342211 0.9999712053062613 0.9998455487773041 0.9994708469410413 0.9986143016079504 0.9969705407493977 0.9941842791906069 0.98987954040974 0.9836899358824059 0.9752857883717809 0.9643954017109466 0.9508192084800389 0.9344367125880007 0.9152070144154019 0.8931642410169756 0.8684094215335494 0.8411003004258139 0.8114403467322836 0.7796678879635208 0.7460459576005712 0.7108531588334811 0.6743756442987432 0.6369001912092349 0.5987082945849412 0.5600711906160255 0.5212457557943646 0.48247131096244444 0.4439674882149067 0.4059334569680495 0.36854889216479886 0.3319770339522551 0.2963699789916535 0.261875949592214 0.22864778488029475 0.1968514346246697 0.16667294354493165 0.1383223499092605 0.1120330897391903 0.08805592006793161 0.06664683672557463 0.04804887824309214 0.032467763945423105 0.020041090766304153 0.010800519368996297 0.004626509028662197 0.0011964351673459904 -7.082718961695422e-5; 0.0 0.0 9.141911056305528e-22 0.0017258866288198675 0.006384348094661891 0.014720253802042015 0.027084888686411165 0.04350777973495859 0.0637649275163413 0.08743934569875944 0.11397310461216442 0.14271187650994513 0.1729433700500834 0.2039306871949977 0.23494109528684004 0.26527028804381697 0.29426202393115164 0.3213230702712095 0.3459335740800823 0.3676532302781406 0.38612383863193656 0.40106897276354997 0.41229151157690874 0.4196697216927663 0.42315246945511215 0.4227540266591201 0.41854884379550666 0.41066659942118544 0.3992877685309184 0.3846398590308741 0.36699433188470937 0.34666406332602073 0.3240010557592135 0.29939398877483514 0.27326515661071893 0.2460663845828833 0.2182736317566618 0.19038010675944506 0.16288780980360199 0.13629747864377106 0.11109697720116149 0.08774813892936445 0.06667202447925373 0.048232298119338206 0.03271602515045203 0.020310533574094233 0.011074319595047769 0.004900037686356889 0.0014692859582479986 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DirectTrajOpt.Objectives.var"#∂²L#28"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}(UnitRange{Int64}[736:743], 750), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}(UnitRange{Int64}[736:743], 750)), DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#51"{Matrix{Float64}, UnitRange{Int64}, Symbol, NamedTrajectories.StructNamedTrajectory.NamedTrajectory{Float64}, Vector{Float64}}([0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 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1.0]), Δt = ([0.1], [0.30000000000000004])), (Ũ⃗ = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], a = [0.0, 0.0], da = [0.0, 0.0]), (a = [0.0, 0.0], da = [0.0, 0.0]), (Ũ⃗ = [0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0],), (Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15]), NamedTuple(), 0, NamedTuple(), NamedTuple(), (:Ũ⃗, :a, :da, :dda, :Δt), (:Ũ⃗, :a, :da), (:dda, :Δt))))), DirectTrajOpt.Objectives.var"#3#7"{DirectTrajOpt.Objectives.Objective, DirectTrajOpt.Objectives.Objective}(DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#24"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∇L#25"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}, Int64}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743], 750), DirectTrajOpt.Objectives.var"#∂²L#28"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}(UnitRange{Int64}[736:743], 750), UnitRange{Int64}[736:743]), 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1.0]), Δt = ([0.1], [0.30000000000000004])), (Ũ⃗ = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], a = [0.0, 0.0], da = [0.0, 0.0]), (a = [0.0, 0.0], da = [0.0, 0.0]), (Ũ⃗ = [0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0],), (Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15]), NamedTuple(), 0, NamedTuple(), NamedTuple(), (:Ũ⃗, :a, :da, :dda, :Δt), (:Ũ⃗, :a, :da), (:dda, :Δt))))), DirectTrajOpt.Objectives.var"#4#8"{DirectTrajOpt.Objectives.Objective, DirectTrajOpt.Objectives.Objective}(DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#24"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∇L#25"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}, Int64}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743], 750), DirectTrajOpt.Objectives.var"#∂²L#28"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}(UnitRange{Int64}[736:743], 750), UnitRange{Int64}[736:743]), 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0.0], a = [0.0, 0.0], da = [0.0, 0.0]), (a = [0.0, 0.0], da = [0.0, 0.0]), (Ũ⃗ = [0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0],), (Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15]), NamedTuple(), 0, NamedTuple(), NamedTuple(), (:Ũ⃗, :a, :da, :dda, :Δt), (:Ũ⃗, :a, :da), (:dda, :Δt))))), DirectTrajOpt.Objectives.var"#3#7"{DirectTrajOpt.Objectives.Objective, DirectTrajOpt.Objectives.Objective}(DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#24"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∇L#25"{Vector{Float64}, 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1.0]), Δt = ([0.1], [0.30000000000000004])), (Ũ⃗ = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], a = [0.0, 0.0], da = [0.0, 0.0]), (a = [0.0, 0.0], da = [0.0, 0.0]), (Ũ⃗ = [0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0],), (Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15]), NamedTuple(), 0, NamedTuple(), NamedTuple(), (:Ũ⃗, :a, :da, :dda, :Δt), (:Ũ⃗, :a, :da), (:dda, :Δt))))), DirectTrajOpt.Objectives.var"#3#7"{DirectTrajOpt.Objectives.Objective, DirectTrajOpt.Objectives.Objective}(DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#24"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∇L#25"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}, Int64}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743], 750), DirectTrajOpt.Objectives.var"#∂²L#28"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}(UnitRange{Int64}[736:743], 750), UnitRange{Int64}[736:743]), 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1.0]), Δt = ([0.1], [0.30000000000000004])), (Ũ⃗ = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], a = [0.0, 0.0], da = [0.0, 0.0]), (a = [0.0, 0.0], da = [0.0, 0.0]), (Ũ⃗ = [0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0],), (Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15]), NamedTuple(), 0, NamedTuple(), NamedTuple(), (:Ũ⃗, :a, :da, :dda, :Δt), (:Ũ⃗, :a, :da), (:dda, :Δt))))), DirectTrajOpt.Objectives.var"#4#8"{DirectTrajOpt.Objectives.Objective, DirectTrajOpt.Objectives.Objective}(DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#24"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∇L#25"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}, Int64}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743], 750), DirectTrajOpt.Objectives.var"#∂²L#28"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}(UnitRange{Int64}[736:743], 750), UnitRange{Int64}[736:743]), 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0.0], a = [0.0, 0.0], da = [0.0, 0.0]), (a = [0.0, 0.0], da = [0.0, 0.0]), (Ũ⃗ = [0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0],), (Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15]), NamedTuple(), 0, NamedTuple(), NamedTuple(), (:Ũ⃗, :a, :da, :dda, :Δt), (:Ũ⃗, :a, :da), (:dda, :Δt))))), DirectTrajOpt.Objectives.var"#3#7"{DirectTrajOpt.Objectives.Objective, DirectTrajOpt.Objectives.Objective}(DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#24"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∇L#25"{Vector{Float64}, 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1.0]), Δt = ([0.1], [0.30000000000000004])), (Ũ⃗ = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], a = [0.0, 0.0], da = [0.0, 0.0]), (a = [0.0, 0.0], da = [0.0, 0.0]), (Ũ⃗ = [0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0],), (Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15]), NamedTuple(), 0, NamedTuple(), NamedTuple(), (:Ũ⃗, :a, :da, :dda, :Δt), (:Ũ⃗, :a, :da), (:dda, :Δt))))), DirectTrajOpt.Objectives.var"#2#6"{DirectTrajOpt.Objectives.Objective, DirectTrajOpt.Objectives.Objective}(DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#24"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∇L#25"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}, Int64}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743], 750), DirectTrajOpt.Objectives.var"#∂²L#28"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}(UnitRange{Int64}[736:743], 750), UnitRange{Int64}[736:743]), 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1.0]), Δt = ([0.1], [0.30000000000000004])), (Ũ⃗ = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], a = [0.0, 0.0], da = [0.0, 0.0]), (a = [0.0, 0.0], da = [0.0, 0.0]), (Ũ⃗ = [0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0],), (Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15]), NamedTuple(), 0, NamedTuple(), NamedTuple(), (:Ũ⃗, :a, :da, :dda, :Δt), (:Ũ⃗, :a, :da), (:dda, :Δt))))), DirectTrajOpt.Objectives.var"#3#7"{DirectTrajOpt.Objectives.Objective, DirectTrajOpt.Objectives.Objective}(DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#24"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∇L#25"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}, Int64}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743], 750), DirectTrajOpt.Objectives.var"#∂²L#28"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}(UnitRange{Int64}[736:743], 750), UnitRange{Int64}[736:743]), 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1.0]), Δt = ([0.1], [0.30000000000000004])), (Ũ⃗ = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], a = [0.0, 0.0], da = [0.0, 0.0]), (a = [0.0, 0.0], da = [0.0, 0.0]), (Ũ⃗ = [0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0],), (Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15]), NamedTuple(), 0, NamedTuple(), NamedTuple(), (:Ũ⃗, :a, :da, :dda, :Δt), (:Ũ⃗, :a, :da), (:dda, :Δt))))), DirectTrajOpt.Objectives.var"#2#6"{DirectTrajOpt.Objectives.Objective, DirectTrajOpt.Objectives.Objective}(DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#24"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∇L#25"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}, Int64}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743], 750), DirectTrajOpt.Objectives.var"#∂²L#28"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}(UnitRange{Int64}[736:743], 750), UnitRange{Int64}[736:743]), 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1.0]), Δt = ([0.1], [0.30000000000000004])), (Ũ⃗ = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], a = [0.0, 0.0], da = [0.0, 0.0]), (a = [0.0, 0.0], da = [0.0, 0.0]), (Ũ⃗ = [0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0],), (Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15]), NamedTuple(), 0, NamedTuple(), NamedTuple(), (:Ũ⃗, :a, :da, :dda, :Δt), (:Ũ⃗, :a, :da), (:dda, :Δt))))), DirectTrajOpt.Objectives.var"#3#7"{DirectTrajOpt.Objectives.Objective, DirectTrajOpt.Objectives.Objective}(DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#24"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∇L#25"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}, Int64}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743], 750), DirectTrajOpt.Objectives.var"#∂²L#28"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}(UnitRange{Int64}[736:743], 750), UnitRange{Int64}[736:743]), 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